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[Axiom-developer] 20080401.01.tpd.patch (CATS integration regression tes
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From: |
daly |
|
Subject: |
[Axiom-developer] 20080401.01.tpd.patch (CATS integration regression testing) |
|
Date: |
Wed, 2 Apr 2008 00:35:43 -0600 |
More integrals
=========================================================================
diff --git a/changelog b/changelog
index a9a8d1b..6f6fcb0 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,7 @@
+20080401 tpd src/input/Makefile add integration regression testing
+20080401 tpd src/input/schaum14.input integrals of x^3+a^3
+20080401 tpd src/input/schaum13.input integrals of sqrt(ax^2+bx+c)
+20080401 tpd src/input/schaum12.input fix typo
20080331 tpd src/input/Makefile add integration regression testing
20080331 tpd src/input/schaum12.input integrals of ax^2+bx+c
20080330 tpd src/input/Makefile add integration regression testing
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet
index e42c5c0..2f109e9 100644
--- a/src/input/Makefile.pamphlet
+++ b/src/input/Makefile.pamphlet
@@ -358,6 +358,7 @@ REGRES= algaggr.regress algbrbf.regress algfacob.regress
alist.regress \
schaum1.regress schaum2.regress schaum3.regress schaum4.regress \
schaum5.regress schaum6.regress schaum7.regress schaum8.regress \
schaum9.regress schaum10.regress schaum11.regress schaum12.regress \
+ schaum13.regress schaum14.regress \
scherk.regress scope.regress seccsc.regress \
segbind.regress seg.regress \
series2.regress series.regress sersolve.regress set.regress \
@@ -633,7 +634,8 @@ FILES= ${OUT}/algaggr.input ${OUT}/algbrbf.input
${OUT}/algfacob.input \
${OUT}/schaum2.input ${OUT}/schaum3.input ${OUT}/schaum4.input \
${OUT}/schaum5.input ${OUT}/schaum6.input ${OUT}/schaum7.input \
${OUT}/schaum8.input ${OUT}/schaum9.input ${OUT}/schaum10.input \
- ${OUT}/schaum11.input ${OUT}/schaum12.input \
+ ${OUT}/schaum11.input ${OUT}/schaum12.input ${OUT}/schaum13.input \
+ ${OUT}/schaum14.input \
${OUT}/saddle.input \
${OUT}/scherk.input ${OUT}/scope.input ${OUT}/seccsc.input \
${OUT}/segbind.input ${OUT}/seg.input ${OUT}/series2.input \
@@ -938,6 +940,7 @@ DOCFILES= \
${DOC}/schaum7.input.dvi ${DOC}/schaum8.input.dvi \
${DOC}/schaum9.input.dvi ${DOC}/schaum10.input.dvi \
${DOC}/schaum11.input.dvi ${DOC}/schaum12.input.dvi \
+ ${DOC}/schaum13.input.dvi ${DOC}/schaum14.input.dvi \
${DOC}/s01eaf.input.dvi ${DOC}/s13aaf.input.dvi \
${DOC}/s13acf.input.dvi ${DOC}/s13adf.input.dvi \
${DOC}/s14aaf.input.dvi ${DOC}/s14abf.input.dvi \
diff --git a/src/input/schaum12.input.pamphlet
b/src/input/schaum12.input.pamphlet
index 6027801..6669ade 100644
--- a/src/input/schaum12.input.pamphlet
+++ b/src/input/schaum12.input.pamphlet
@@ -321,13 +321,14 @@ $$
)clear all
--S 7 of 15
-aa:=integrate(1/(x^n*(ax^2+bx+c)),x)
+aa:=integrate(1/(x^n*(a*x^2+b*x+c)),x)
--R
--R
---R x
---R (1) - ------------------------------------------
---R 2 2 n log(x)
---R ((c + bx + ax )n - c - bx - ax )%e
+--R x
+--R ++ 1
+--R (1) | -------------------- d%N
+--R ++ 2 n
+--R (c + %N b + %N a)%N
--R Type: Union(Expression
Integer,...)
--E
@
diff --git a/src/input/schaum13.input.pamphlet
b/src/input/schaum13.input.pamphlet
new file mode 100644
index 0000000..04551e6
--- /dev/null
+++ b/src/input/schaum13.input.pamphlet
@@ -0,0 +1,1266 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum13.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.280~~~~~$\displaystyle
+\int{\frac{dx}{\sqrt{ax^2+bx+c}}}$}
+$$\int{\frac{1}{\sqrt{ax^2+bx+c}}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{1}{\sqrt{a}}\ln\left(2\sqrt{a}\sqrt{ax^2+bx+c}+2ax+b\right)\\
+\\
+\displaystyle
+-\frac{1}{\sqrt{-a}}\sin{-1}\left(\frac{2ax+b}{\sqrt{b^2-4ac}}\right)\\
+\\
+\displaystyle
+\frac{1}{\sqrt{a}}\sinh^{-1}\left(\frac{2ax+b}{\sqrt{4ac-b^2}}\right)
+\end{array}
+\right.
+$$
+<<*>>=
+)spool schaum13.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 19
+aa:=integrate(1/sqrt(a*x^2+b*x+c),x)
+--R
+--R
+--R (1)
+--R [
+--R log
+--R +--------------+
+--R +-+ +-+ | 2 +-+
+--R (2\|a \|c - 2a x)\|a x + b x + c + 2a x\|c
+--R +
+--R 2 +-+
+--R (- 2a x - b x - 2c)\|a
+--R /
+--R +--------------+
+--R +-+ | 2
+--R 2\|c \|a x + b x + c - b x - 2c
+--R /
+--R +-+
+--R \|a
+--R ,
+--R +--------------+
+--R +---+ | 2 +---+ +-+
+--R \|- a \|a x + b x + c - \|- a \|c
+--R 2atan(------------------------------------)
+--R a x
+--R -------------------------------------------]
+--R +---+
+--R \|- a
+--R Type: Union(List Expression
Integer,...)
+--E
+@
+
+\section{\cite{1}:14.281~~~~~$\displaystyle
+\int{\frac{x~dx}{\sqrt{ax^2+bx+c}}}$}
+$$\int{\frac{x}{\sqrt{ax^2+bx+c}}}=
+\frac{\sqrt{ax^2+bx+c}}{a}-\frac{b}{2a}\int{\frac{1}{\sqrt{ax^2+bx+c}}}
+$$
+<<*>>=
+)clear all
+
+--S 2 of 19
+aa:=integrate(x/sqrt(a*x^2+b*x+c),x)
+--R
+--R
+--R (1)
+--R [
+--R +--------------+
+--R +-+ | 2 2
+--R (2b\|c \|a x + b x + c - b x - 2b c)
+--R *
+--R log
+--R +--------------+
+--R +-+ +-+ | 2 +-+
+--R (2\|a \|c + 2a x)\|a x + b x + c - 2a x\|c
+--R +
+--R 2 +-+
+--R (- 2a x - b x - 2c)\|a
+--R /
+--R +--------------+
+--R +-+ | 2
+--R 2\|c \|a x + b x + c - b x - 2c
+--R +
+--R +--------------+
+--R +-+ | 2 2 +-+ +-+
+--R - 2b x\|a \|a x + b x + c + (4a x + 2b x)\|a \|c
+--R /
+--R +--------------+
+--R +-+ +-+ | 2 +-+
+--R 4a\|a \|c \|a x + b x + c + (- 2a b x - 4a c)\|a
+--R ,
+--R
+--R +--------------+
+--R +-+ | 2 2
+--R (- 2b\|c \|a x + b x + c + b x + 2b c)
+--R *
+--R +--------------+
+--R +---+ | 2 +---+ +-+
+--R \|- a \|a x + b x + c - \|- a \|c
+--R atan(------------------------------------)
+--R a x
+--R +
+--R +--------------+
+--R +---+ | 2 2 +---+ +-+
+--R - b x\|- a \|a x + b x + c + (2a x + b x)\|- a \|c
+--R /
+--R +--------------+
+--R +---+ +-+ | 2 +---+
+--R 2a\|- a \|c \|a x + b x + c + (- a b x - 2a c)\|- a
+--R ]
+--R Type: Union(List Expression
Integer,...)
+--E
+@
+
+\section{\cite{1}:14.282~~~~~$\displaystyle
+\int{\frac{x^2dx}{\sqrt{ax^2+bx+c}}}$}
+$$\int{\frac{x^2}{\sqrt{ax^2+bx+c}}}=
+\frac{2ax-3b}{4a^2}\sqrt{ax^2+bx+c}+\frac{3b^2-4ac}{8a^2}
+\int{\frac{1}{\sqrt{ax^2+bx+c}}}
+$$
+<<*>>=
+)clear all
+
+--S 3 of 19
+aa:=integrate(x^2/(a*x^2+b*x+c),x)
+--R
+--R
+--R (1)
+--R [
+--R 2
+--R (2a c - b )
+--R *
+--R log
+--R +-----------+
+--R 2 2 2 | 2 2
2
+--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (- 8a c + 2a
b )x
+--R +
+--R 3
+--R - 4a b c + b
+--R /
+--R 2
+--R a x + b x + c
+--R +
+--R +-----------+
+--R 2 | 2
+--R (- b log(a x + b x + c) + 2a x)\|- 4a c + b
+--R /
+--R +-----------+
+--R 2 | 2
+--R 2a \|- 4a c + b
+--R ,
+--R
+--R +---------+
+--R | 2
+--R 2 (2a x + b)\|4a c - b
+--R (- 4a c + 2b )atan(----------------------)
+--R 2
+--R 4a c - b
+--R +
+--R +---------+
+--R 2 | 2
+--R (- b log(a x + b x + c) + 2a x)\|4a c - b
+--R /
+--R +---------+
+--R 2 | 2
+--R 2a \|4a c - b
+--R ]
+--R Type: Union(List Expression
Integer,...)
+--E
+@
+
+\section{\cite{1}:14.283~~~~~$\displaystyle
+\int{\frac{dx}{x\sqrt{ax^2+bx+c}}}$}
+$$\int{\frac{1}{x\sqrt{ax^2+bx+c}}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+-\frac{1}{\sqrt{c}}
+\ln\left(\frac{2\sqrt{c}{\sqrt{ax^2+bx+c}}+bx+2c}{x}\right)\\
+\\
+\displaystyle
+\frac{1}{\sqrt{-c}}\sin^{-1}\left(\frac{bx+2c}{|x|\sqrt{b^2-4ac}}\right)\\
+\\
+\displaystyle
+-\frac{1}{\sqrt{c}}\sinh^{-1}\left(\frac{bx+2c}{|x|\sqrt{4ac-b^2}}\right)
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 4 of 19
+aa:=integrate(1/x*(a*x^2+b*x+c),x)
+--R
+--R
+--R 2
+--R 2c log(x) + a x + 2b x
+--R (1) -----------------------
+--R 2
+--R Type: Union(Expression
Integer,...)
+--E
+@
+
+\section{\cite{1}:14.284~~~~~$\displaystyle
+\int{\frac{dx}{x^2\sqrt{ax^2+bx+c}}}$}
+$$\int{\frac{1}{x^2\sqrt{ax^2+bx+c}}}=
+-\frac{\sqrt{ax^2+bx+c}}{cx}-\frac{b}{2c}\int{\frac{1}{x\sqrt{ax^2+bx+c}}}
+$$
+<<*>>=
+)clear all
+
+--S 5 of 19
+aa:=integrate(1/(x^2*(a*x^2+b*x+c)),x)
+--R
+--R
+--R (1)
+--R [
+--R 2
+--R (2a c - b )x
+--R *
+--R log
+--R +-----------+
+--R 2 2 2 | 2 2
2
+--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (- 8a c + 2a
b )x
+--R +
+--R 3
+--R - 4a b c + b
+--R /
+--R 2
+--R a x + b x + c
+--R +
+--R +-----------+
+--R 2 | 2
+--R (b x log(a x + b x + c) - 2b x log(x) - 2c)\|- 4a c + b
+--R /
+--R +-----------+
+--R 2 | 2
+--R 2c x\|- 4a c + b
+--R ,
+--R
+--R +---------+
+--R | 2
+--R 2 (2a x + b)\|4a c - b
+--R (- 4a c + 2b )x atan(----------------------)
+--R 2
+--R 4a c - b
+--R +
+--R +---------+
+--R 2 | 2
+--R (b x log(a x + b x + c) - 2b x log(x) - 2c)\|4a c - b
+--R /
+--R +---------+
+--R 2 | 2
+--R 2c x\|4a c - b
+--R ]
+--R Type: Union(List Expression
Integer,...)
+--E
+@
+
+\section{\cite{1}:14.285~~~~~$\displaystyle
+\int{\sqrt{ax^2+bx+c}}~dx$}
+$$\int{\sqrt{ax^2+bx+c}}=
+\frac{(2ax+b)\sqrt{ax^2+bx+c}}{4a}+
+\frac{4ac-b^2}{8a}\int{\frac{1}{\sqrt{ax^2+bx+c}}}
+$$
+<<*>>=
+)clear all
+
+--S 6 of 19
+aa:=integrate(sqrt(a*x^2+b*x+c),x)
+--R
+--R
+--R (1)
+--R [
+--R +--------------+
+--R 3 2 2 +-+ | 2
+--R ((16a b c - 4b )x + 32a c - 8b c)\|c \|a x + b x + c
+--R +
+--R 2 2 4 2 2 3 3 2 2
+--R (- 16a c + b )x + (- 32a b c + 8b c)x - 32a c + 8b c
+--R *
+--R log
+--R +--------------+
+--R +-+ +-+ | 2 +-+
+--R (2\|a \|c - 2a x)\|a x + b x + c + 2a x\|c
+--R +
+--R 2 +-+
+--R (- 2a x - b x - 2c)\|a
+--R /
+--R +--------------+
+--R +-+ | 2
+--R 2\|c \|a x + b x + c - b x - 2c
+--R +
+--R 2 2 3 3 2 2 2
+-+
+--R ((- 16a c - 4a b )x + (- 40a b c - 2b )x + (- 32a c - 8b
c)x)\|a
+--R *
+--R +--------------+
+--R | 2
+--R \|a x + b x + c
+--R +
+--R 2 4 2 2 3 3 2
+--R 16a b x + (32a c + 24a b )x + (56a b c + 6b )x
+--R +
+--R 2 2
+--R (32a c + 8b c)x
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R +--------------+
+--R +-+ +-+ | 2
+--R (32a b x + 64a c)\|a \|c \|a x + b x + c
+--R +
+--R 2 2 2 2 +-+
+--R ((- 32a c - 8a b )x - 64a b c x - 64a c )\|a
+--R ,
+--R
+--R +--------------+
+--R 3 2 2 +-+ | 2
+--R ((16a b c - 4b )x + 32a c - 8b c)\|c \|a x + b x + c
+--R +
+--R 2 2 4 2 2 3 3 2 2
+--R (- 16a c + b )x + (- 32a b c + 8b c)x - 32a c + 8b c
+--R *
+--R +--------------+
+--R +---+ | 2 +---+ +-+
+--R \|- a \|a x + b x + c - \|- a \|c
+--R atan(------------------------------------)
+--R a x
+--R +
+--R 2 2 3 3 2 2 2
+---+
+--R ((- 8a c - 2a b )x + (- 20a b c - b )x + (- 16a c - 4b
c)x)\|- a
+--R *
+--R +--------------+
+--R | 2
+--R \|a x + b x + c
+--R +
+--R 2 4 2 2 3 3 2 2 2
+--R (8a b x + (16a c + 12a b )x + (28a b c + 3b )x + (16a c + 4b
c)x)
+--R *
+--R +---+ +-+
+--R \|- a \|c
+--R /
+--R +--------------+
+--R +---+ +-+ | 2
+--R (16a b x + 32a c)\|- a \|c \|a x + b x + c
+--R +
+--R 2 2 2 2 +---+
+--R ((- 16a c - 4a b )x - 32a b c x - 32a c )\|- a
+--R ]
+--R Type: Union(List Expression
Integer,...)
+--E
+@
+
+\section{\cite{1}:14.286~~~~~$\displaystyle
+\int{x\sqrt{ax^2+bx+c}}~dx$}
+$$
+\begin{array}{rl}
+\displaystyle
+\int{x\sqrt{ax^2+bx+c}}=&\displaystyle\frac{(ax^2+bx+c)^{3/2}}{3a}\\
+&\\
+&\displaystyle-\frac{b(2ax+b)}{8a^2}\sqrt{ax^2+bx+c}\\
+&\\
+&\displaystyle-\frac{b(4ac-b^2)}{16a^2}\int{\frac{1}{\sqrt{ax^2+bx+c}}}
+\end{array}
+$$
+<<*>>=
+)clear all
+
+--S 7 of 19
+aa:=integrate(x*sqrt(a*x^2+b*x+c),x)
+--R
+--R
+--R (1)
+--R [
+--R 2 2 3 5 2 2 2 4
+--R (96a b c + 48a b c - 18b )x + (384a b c - 96b c)x
+--R +
+--R 3 3 2
+--R 384a b c - 96b c
+--R *
+--R +--------------+
+--R +-+ | 2
+--R \|c \|a x + b x + c
+--R +
+--R 2 2 2 4 6 3
+--R (- 144a b c + 24a b c + 3b )x
+--R +
+--R 2 3 3 2 5 2 2 3 4 2
+--R (- 288a b c - 144a b c + 54b c)x + (- 576a b c + 144b c )x
+--R +
+--R 4 3 3
+--R - 384a b c + 96b c
+--R *
+--R log
+--R +--------------+
+--R +-+ +-+ | 2 +-+
+--R (2\|a \|c + 2a x)\|a x + b x + c - 2a x\|c
+--R +
+--R 2 +-+
+--R (- 2a x - b x - 2c)\|a
+--R /
+--R +--------------+
+--R +-+ | 2
+--R 2\|c \|a x + b x + c - b x - 2c
+--R +
+--R 3 2 3 5 3 2 2 2 4 4
+--R (- 192a b c - 16a b )x + (- 384a c - 336a b c - 4a b )x
+--R +
+--R 2 2 3 5 3
+--R (- 1056a b c - 16a b c + 6b )x
+--R +
+--R 2 3 2 2 4 2 3 3 2
+--R (- 768a c - 288a b c + 72b c)x + (- 384a b c + 96b c )x
+--R *
+--R +--------------+
+--R +-+ | 2
+--R \|a \|a x + b x + c
+--R +
+--R 4 3 2 6 3 2 3 5
+--R (128a c + 96a b )x + (672a b c + 120a b )x
+--R +
+--R 3 2 2 2 4 4 2 2 3 5
3
+--R (768a c + 816a b c - 12a b )x + (1632a b c + 64a b c - 30b
)x
+--R +
+--R 2 3 2 2 4 2 3 3 2
+--R (768a c + 480a b c - 120b c)x + (384a b c - 96b c )x
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 3 2 2 2 2 2 2 +-+ +-+
+--R ((384a c + 288a b )x + 1536a b c x + 1536a c )\|a \|c
+--R *
+--R +--------------+
+--R | 2
+--R \|a x + b x + c
+--R +
+--R 3 2 3 3 3 2 2 2 2 2
2
+--R (- 576a b c - 48a b )x + (- 1152a c - 864a b c)x - 2304a b
c x
+--R +
+--R 2 3
+--R - 1536a c
+--R *
+--R +-+
+--R \|a
+--R ,
+--R
+--R 2 2 3 5 2 2 2 4
+--R (- 96a b c - 48a b c + 18b )x + (- 384a b c + 96b c)x
+--R +
+--R 3 3 2
+--R - 384a b c + 96b c
+--R *
+--R +--------------+
+--R +-+ | 2
+--R \|c \|a x + b x + c
+--R +
+--R 2 2 2 4 6 3 2 3 3 2 5
2
+--R (144a b c - 24a b c - 3b )x + (288a b c + 144a b c - 54b
c)x
+--R +
+--R 2 3 4 2 4 3 3
+--R (576a b c - 144b c )x + 384a b c - 96b c
+--R *
+--R +--------------+
+--R +---+ | 2 +---+ +-+
+--R \|- a \|a x + b x + c - \|- a \|c
+--R atan(------------------------------------)
+--R a x
+--R +
+--R 3 2 3 5 3 2 2 2 4 4
+--R (- 96a b c - 8a b )x + (- 192a c - 168a b c - 2a b )x
+--R +
+--R 2 2 3 5 3 2 3 2 2 4
2
+--R (- 528a b c - 8a b c + 3b )x + (- 384a c - 144a b c + 36b
c)x
+--R +
+--R 3 3 2
+--R (- 192a b c + 48b c )x
+--R *
+--R +--------------+
+--R +---+ | 2
+--R \|- a \|a x + b x + c
+--R +
+--R 4 3 2 6 3 2 3 5
+--R (64a c + 48a b )x + (336a b c + 60a b )x
+--R +
+--R 3 2 2 2 4 4 2 2 3 5 3
+--R (384a c + 408a b c - 6a b )x + (816a b c + 32a b c - 15b )x
+--R +
+--R 2 3 2 2 4 2 3 3 2
+--R (384a c + 240a b c - 60b c)x + (192a b c - 48b c )x
+--R *
+--R +---+ +-+
+--R \|- a \|c
+--R /
+--R 3 2 2 2 2 2 2 +---+ +-+
+--R ((192a c + 144a b )x + 768a b c x + 768a c )\|- a \|c
+--R *
+--R +--------------+
+--R | 2
+--R \|a x + b x + c
+--R +
+--R 3 2 3 3 3 2 2 2 2 2 2
+--R (- 288a b c - 24a b )x + (- 576a c - 432a b c)x - 1152a b c
x
+--R +
+--R 2 3
+--R - 768a c
+--R *
+--R +---+
+--R \|- a
+--R ]
+--R Type: Union(List Expression
Integer,...)
+--E
+@
+
+\section{\cite{1}:14.287~~~~~$\displaystyle
+\int{x^2\sqrt{ax^2+bx+c}}~dx$}
+$$\int{x^2\sqrt{ax^2+bx+c}}=
+\frac{6ax-5b}{24a^2}(ax^2+bx+c)^{3/2}+
+\frac{5b^2-4ac}{16a^2}\int{\sqrt{ax^2+bx+c}}
+$$
+<<*>>=
+)clear all
+
+--S 8 of 19
+aa:=integrate(x^2*sqrt(a*x^2+b*x+c),x)
+--R
+--R
+--R (1)
+--R [
+--R 3 3 2 3 2 5 7 3
+--R (1536a b c - 1920a b c - 96a b c + 120b )x
+--R +
+--R 3 4 2 2 3 4 2 6 2
+--R (3072a c - 768a b c - 4800a b c + 1200b c)x
+--R +
+--R 2 4 3 3 5 2 2 5
2 4
+--R (9216a b c - 13824a b c + 2880b c )x + 6144a c - 9216a
b c
+--R +
+--R 4 3
+--R 1920b c
+--R *
+--R +--------------+
+--R +-+ | 2
+--R \|c \|a x + b x + c
+--R +
+--R 4 4 2 4 2 6 8 4
+--R (- 768a c + 1440a b c - 288a b c - 15b )x
+--R +
+--R 3 4 2 3 3 5 2 7 3
+--R (- 6144a b c + 7680a b c + 384a b c - 480b c)x
+--R +
+--R 3 5 2 2 4 4 3 6 2 2
+--R (- 6144a c + 1536a b c + 9600a b c - 2400b c )x
+--R +
+--R 2 5 3 4 5 3 2 6
2 5
+--R (- 12288a b c + 18432a b c - 3840b c )x - 6144a c + 9216a b
c
+--R +
+--R 4 4
+--R - 1920b c
+--R *
+--R log
+--R +--------------+
+--R +-+ +-+ | 2 +-+
+--R (2\|a \|c + 2a x)\|a x + b x + c - 2a x\|c
+--R +
+--R 2 +-+
+--R (- 2a x - b x - 2c)\|a
+--R /
+--R +--------------+
+--R +-+ | 2
+--R 2\|c \|a x + b x + c - b x - 2c
+--R +
+--R 5 2 4 2 3 4 7
+--R (- 1536a c - 2304a b c - 96a b )x
+--R +
+--R 4 2 3 3 2 5 6
+--R (- 12544a b c - 3456a b c - 16a b )x
+--R +
+--R 4 3 3 2 2 2 4 6 5
+--R (- 13056a c - 18240a b c - 80a b c + 20a b )x
+--R +
+--R 3 3 2 3 2 5 7 4
+--R (- 31104a b c + 480a b c + 24a b c - 30b )x
+--R +
+--R 3 4 2 2 3 4 2 6 3
+--R (- 18432a c + 768a b c + 2816a b c - 720b c)x
+--R +
+--R 2 4 3 3 5 2 2
+--R (- 7680a b c + 11520a b c - 2400b c )x
+--R +
+--R 2 5 2 4 4 3
+--R (- 6144a c + 9216a b c - 1920b c )x
+--R *
+--R +--------------+
+--R +-+ | 2
+--R \|a \|a x + b x + c
+--R +
+--R 5 4 3 8 5 2 4 2 3 4 7
+--R (3072a b c + 768a b )x + (6144a c + 11264a b c + 896a b )x
+--R +
+--R 4 2 3 3 2 5 6
+--R (30208a b c + 9984a b c - 32a b )x
+--R +
+--R 4 3 3 2 2 2 4 6 5
+--R (21504a c + 31488a b c - 320a b c + 80a b )x
+--R +
+--R 3 3 2 3 2 5 7 4
+--R (42624a b c - 4896a b c + 152a b c + 210b )x
+--R +
+--R 3 4 2 2 3 4 2 6 3
+--R (21504a c - 2304a b c - 6464a b c + 1680b c)x
+--R +
+--R 2 4 3 3 5 2 2
+--R (10752a b c - 16128a b c + 3360b c )x
+--R +
+--R 2 5 2 4 4 3
+--R (6144a c - 9216a b c + 1920b c )x
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 4 3 3 3 4 2 3 2 2
+--R (12288a b c + 3072a b )x + (24576a c + 30720a b c)x
+--R +
+--R 3 2 3 3
+--R 73728a b c x + 49152a c
+--R *
+--R +--------------+
+--R +-+ +-+ | 2
+--R \|a \|c \|a x + b x + c
+--R +
+--R 5 2 4 2 3 4 4
+--R (- 6144a c - 9216a b c - 384a b )x
+--R +
+--R 4 2 3 3 3 4 3 3 2 2 2
+--R (- 49152a b c - 12288a b c)x + (- 49152a c - 61440a b c )x
+--R +
+--R 3 3 3 4
+--R - 98304a b c x - 49152a c
+--R *
+--R +-+
+--R \|a
+--R ,
+--R
+--R 3 3 2 3 2 5 7 3
+--R (- 1536a b c + 1920a b c + 96a b c - 120b )x
+--R +
+--R 3 4 2 2 3 4 2 6 2
+--R (- 3072a c + 768a b c + 4800a b c - 1200b c)x
+--R +
+--R 2 4 3 3 5 2 2 5
+--R (- 9216a b c + 13824a b c - 2880b c )x - 6144a c
+--R +
+--R 2 4 4 3
+--R 9216a b c - 1920b c
+--R *
+--R +--------------+
+--R +-+ | 2
+--R \|c \|a x + b x + c
+--R +
+--R 4 4 2 4 2 6 8 4
+--R (768a c - 1440a b c + 288a b c + 15b )x
+--R +
+--R 3 4 2 3 3 5 2 7 3
+--R (6144a b c - 7680a b c - 384a b c + 480b c)x
+--R +
+--R 3 5 2 2 4 4 3 6 2 2
+--R (6144a c - 1536a b c - 9600a b c + 2400b c )x
+--R +
+--R 2 5 3 4 5 3 2 6 2 5
+--R (12288a b c - 18432a b c + 3840b c )x + 6144a c - 9216a b c
+--R +
+--R 4 4
+--R 1920b c
+--R *
+--R +--------------+
+--R +---+ | 2 +---+ +-+
+--R \|- a \|a x + b x + c - \|- a \|c
+--R atan(------------------------------------)
+--R a x
+--R +
+--R 5 2 4 2 3 4 7
+--R (- 768a c - 1152a b c - 48a b )x
+--R +
+--R 4 2 3 3 2 5 6
+--R (- 6272a b c - 1728a b c - 8a b )x
+--R +
+--R 4 3 3 2 2 2 4 6 5
+--R (- 6528a c - 9120a b c - 40a b c + 10a b )x
+--R +
+--R 3 3 2 3 2 5 7 4
+--R (- 15552a b c + 240a b c + 12a b c - 15b )x
+--R +
+--R 3 4 2 2 3 4 2 6 3
+--R (- 9216a c + 384a b c + 1408a b c - 360b c)x
+--R +
+--R 2 4 3 3 5 2 2
+--R (- 3840a b c + 5760a b c - 1200b c )x
+--R +
+--R 2 5 2 4 4 3
+--R (- 3072a c + 4608a b c - 960b c )x
+--R *
+--R +--------------+
+--R +---+ | 2
+--R \|- a \|a x + b x + c
+--R +
+--R 5 4 3 8 5 2 4 2 3 4 7
+--R (1536a b c + 384a b )x + (3072a c + 5632a b c + 448a b )x
+--R +
+--R 4 2 3 3 2 5 6
+--R (15104a b c + 4992a b c - 16a b )x
+--R +
+--R 4 3 3 2 2 2 4 6 5
+--R (10752a c + 15744a b c - 160a b c + 40a b )x
+--R +
+--R 3 3 2 3 2 5 7 4
+--R (21312a b c - 2448a b c + 76a b c + 105b )x
+--R +
+--R 3 4 2 2 3 4 2 6 3
+--R (10752a c - 1152a b c - 3232a b c + 840b c)x
+--R +
+--R 2 4 3 3 5 2 2
+--R (5376a b c - 8064a b c + 1680b c )x
+--R +
+--R 2 5 2 4 4 3
+--R (3072a c - 4608a b c + 960b c )x
+--R *
+--R +---+ +-+
+--R \|- a \|c
+--R /
+--R 4 3 3 3 4 2 3 2 2
+--R (6144a b c + 1536a b )x + (12288a c + 15360a b c)x
+--R +
+--R 3 2 3 3
+--R 36864a b c x + 24576a c
+--R *
+--R +--------------+
+--R +---+ +-+ | 2
+--R \|- a \|c \|a x + b x + c
+--R +
+--R 5 2 4 2 3 4 4
+--R (- 3072a c - 4608a b c - 192a b )x
+--R +
+--R 4 2 3 3 3 4 3 3 2 2 2
+--R (- 24576a b c - 6144a b c)x + (- 24576a c - 30720a b c )x
+--R +
+--R 3 3 3 4
+--R - 49152a b c x - 24576a c
+--R *
+--R +---+
+--R \|- a
+--R ]
+--R Type: Union(List Expression
Integer,...)
+--E
+@
+
+\section{\cite{1}:14.288~~~~~$\displaystyle
+\int{\frac{\sqrt{ax^2+bx+c}}{x}}~dx$}
+$$\int{\frac{\sqrt{ax^2+bx+c}}{x}}=
+\sqrt{ax^2+bx+c}+\frac{b}{2}\int{\frac{1}{\sqrt{ax^2+bx+c}}}
++c\int{\frac{1}{x\sqrt{ax^2+bx+c}}}
+$$
+<<*>>=
+)clear all
+
+--S 9 of 19
+aa:=integrate(sqrt(a*x^2+b*x+c)/x,x)
+--R
+--R
+--R (1)
+--R [
+--R +--------------+
+--R +-+ | 2 +-+ +-+
+--R (4c\|a \|a x + b x + c + (- 2b x - 4c)\|a \|c )
+--R *
+--R +--------------+
+--R +-+ | 2
+--R 2\|c \|a x + b x + c - b x - 2c
+--R log(---------------------------------)
+--R +-+
+--R 2x\|c
+--R +
+--R +--------------+
+--R +-+ | 2 2
+--R (2b\|c \|a x + b x + c - b x - 2b c)
+--R *
+--R log
+--R 2 +-+ 2 2 +-+
+--R ((- 2a b x - 8a c x)\|c + (4a c x + 4b c x + 8c )\|a
)
+--R *
+--R +--------------+
+--R | 2
+--R \|a x + b x + c
+--R +
+--R 3 2 2 2 +-+ +-+
2 3
+--R (- 2a b x + (- 8a c - b )x - 8b c x - 8c )\|a \|c + 4a
c x
+--R +
+--R 2 2
+--R 6a b c x + 8a c x
+--R /
+--R +--------------+
+--R 2 | 2
+--R (4b c x + 8c )\|a x + b x + c
+--R +
+--R 2 2 2 +-+
+--R ((- 4a c - b )x - 8b c x - 8c )\|c
+--R +
+--R +--------------+
+--R +-+ | 2 2 +-+ +-+
+--R - 2b x\|a \|a x + b x + c + (4a x + 2b x)\|a \|c
+--R /
+--R +--------------+
+--R +-+ +-+ | 2 +-+
+--R 4\|a \|c \|a x + b x + c + (- 2b x - 4c)\|a
+--R ,
+--R
+--R +--------------+
+--R +---+ | 2 +---+ +-+
+--R (2c\|- a \|a x + b x + c + (- b x - 2c)\|- a \|c )
+--R *
+--R +--------------+
+--R +-+ | 2
+--R 2\|c \|a x + b x + c - b x - 2c
+--R log(---------------------------------)
+--R +-+
+--R 2x\|c
+--R +
+--R +--------------+
+--R +-+ | 2 2
+--R (2b\|c \|a x + b x + c - b x - 2b c)
+--R *
+--R +--------------+
+--R +---+ +-+ | 2 +---+
+--R \|- a \|c \|a x + b x + c - c\|- a
+--R atan(-------------------------------------)
+--R +-+
+--R a x\|c
+--R +
+--R +--------------+
+--R +---+ | 2 2 +---+ +-+
+--R - b x\|- a \|a x + b x + c + (2a x + b x)\|- a \|c
+--R /
+--R +--------------+
+--R +---+ +-+ | 2 +---+
+--R 2\|- a \|c \|a x + b x + c + (- b x - 2c)\|- a
+--R ]
+--R Type: Union(List Expression
Integer,...)
+--E
+@
+
+\section{\cite{1}:14.289~~~~~$\displaystyle
+\int{\frac{\sqrt{ax^2+bx+c}}{x^2}}~dx$}
+$$\int{\frac{\sqrt{ax^2+bx+c}}{x^2}}=
+-\frac{\sqrt{ax^2+bx+c}}{x^2}
++a\int{\frac{1}{\sqrt{ax^2+bx+c}}}
++\frac{b}{2}\int{\frac{1}{x\sqrt{ax^2+bx+c}}}
+$$
+<<*>>=
+)clear all
+
+--S 10 of 19
+aa:=integrate(sqrt(a*x^2+b*x+c)/x^2,x)
+--R
+--R
+--R (1)
+--R [
+--R +--------------+
+--R +-+ | 2 2 2
+--R (4b x\|c \|a x + b x + c - 2b x - 4b c x)
+--R *
+--R +--------------+
+--R | 2 +-+
+--R 2c\|a x + b x + c + (- b x - 2c)\|c
+--R log(--------------------------------------)
+--R 2c x
+--R +
+--R +--------------+
+--R +-+ | 2 2 +-+ +-+
+--R (8c x\|a \|a x + b x + c + (- 4b x - 8c x)\|a \|c )
+--R *
+--R +--------------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (2\|c - 2x\|a )\|a x + b x + c + 2x\|a \|c - 2a x - b x -
2c
+--R
log(-----------------------------------------------------------------)
+--R +--------------+
+--R +-+ | 2
+--R 2\|c \|a x + b x + c - b x - 2c
+--R +
+--R +--------------+
+--R +-+ | 2 2 2 2
+--R (2b x + 8c)\|c \|a x + b x + c + (- 8a c + b )x - 6b c x - 8c
+--R /
+--R +--------------+
+--R | 2 2 +-+
+--R 8c x\|a x + b x + c + (- 4b x - 8c x)\|c
+--R ,
+--R
+--R +--------------+
+--R +-+ | 2 2 2
+--R (4b x\|c \|a x + b x + c - 2b x - 4b c x)
+--R *
+--R +--------------+
+--R | 2 +-+
+--R 2c\|a x + b x + c + (- b x - 2c)\|c
+--R log(--------------------------------------)
+--R 2c x
+--R +
+--R +--------------+
+--R +---+ | 2 2 +---+ +-+
+--R (16c x\|- a \|a x + b x + c + (- 8b x - 16c x)\|- a \|c )
+--R *
+--R +--------------+
+--R | 2 +-+
+--R \|a x + b x + c - \|c
+--R atan(------------------------)
+--R +---+
+--R x\|- a
+--R +
+--R +--------------+
+--R +-+ | 2 2 2 2
+--R (2b x + 8c)\|c \|a x + b x + c + (- 8a c + b )x - 6b c x - 8c
+--R /
+--R +--------------+
+--R | 2 2 +-+
+--R 8c x\|a x + b x + c + (- 4b x - 8c x)\|c
+--R ]
+--R Type: Union(List Expression
Integer,...)
+--E
+@
+
+\section{\cite{1}:14.290~~~~~$\displaystyle
+\int{\frac{dx}{(ax^2+bx+c)^{3/2}}}$}
+$$
+\int{\frac{1}{(ax^2+bx+c)^{3/2}}}=
+\frac{2(2ax+b)}{(4ac-b^2)\sqrt{ax^2+bx+c}}
+$$
+<<*>>=
+)clear all
+
+--S 11 of 19
+aa:=integrate(1/(a*x^2+b*x+c)^(3/2),x)
+--R
+--R
+--R +--------------+
+--R | 2 +-+
+--R - 2x\|a x + b x + c + 2x\|c
+--R (1) --------------------------------------------------------
+--R +--------------+
+--R +-+ | 2 2 2
+--R (b x + 2c)\|c \|a x + b x + c - 2a c x - 2b c x - 2c
+--R Type: Union(Expression
Integer,...)
+--E
+@
+
+\section{\cite{1}:14.291~~~~~$\displaystyle
+\int{\frac{x~dx}{(ax^2+bx+c)^{3/2}}}$}
+$$\int{\frac{x}{(ax^2+bx+c)^{3/2}}}=
+\frac{2(bx+2c)}{(b^2-4ac)\sqrt{ax^2+bx+c}}
+$$
+<<*>>=
+)clear all
+
+--S 12 of 19
+aa:=integrate(x/(a*x^2+b*x+c)^(3/2),x)
+--R
+--R
+--R 2 +-+
+--R 2x \|c
+--R (1) --------------------------------------------------------
+--R +--------------+
+--R +-+ | 2 2 2
+--R (b x + 2c)\|c \|a x + b x + c - 2a c x - 2b c x - 2c
+--R Type: Union(Expression
Integer,...)
+--E
+@
+
+\section{\cite{1}:14.292~~~~~$\displaystyle
+\int{\frac{x^2~dx}{(ax^2+bx+c)^{3/2}}}$}
+$$\int{\frac{x^2}{(ax^2+bx+c)^{3/2}}}=
+\frac{(2b^2-4ac)x+2bc}{a(4ac-b^2)\sqrt{ax^2+bx+c}}
++\frac{1}{a}\int{\frac{1}{\sqrt{ax^2+bx+c}}}
+$$
+<<*>>=
+)clear all
+
+--S 13 of 19
+aa:=integrate(x^2/(a*x^2+b*x+c)^(3/2),x)
+--R
+--R
+--R (1)
+--R [
+--R +--------------+
+--R +-+ | 2 2 2
+--R ((b x + 2c)\|c \|a x + b x + c - 2a c x - 2b c x - 2c )
+--R *
+--R log
+--R +--------------+
+--R +-+ +-+ | 2 +-+
+--R (2\|a \|c - 2a x)\|a x + b x + c + 2a x\|c
+--R +
+--R 2 +-+
+--R (- 2a x - b x - 2c)\|a
+--R /
+--R +--------------+
+--R +-+ | 2
+--R 2\|c \|a x + b x + c - b x - 2c
+--R +
+--R +--------------+
+--R +-+ | 2 2 +-+ +-+
+--R 2c x\|a \|a x + b x + c + (- 2b x - 2c x)\|a \|c
+--R /
+--R +--------------+
+--R +-+ +-+ | 2
+--R (a b x + 2a c)\|a \|c \|a x + b x + c
+--R +
+--R 2 2 2 +-+
+--R (- 2a c x - 2a b c x - 2a c )\|a
+--R ,
+--R
+--R +--------------+
+--R +-+ | 2 2 2
+--R ((2b x + 4c)\|c \|a x + b x + c - 4a c x - 4b c x - 4c )
+--R *
+--R +--------------+
+--R +---+ | 2 +---+ +-+
+--R \|- a \|a x + b x + c - \|- a \|c
+--R atan(------------------------------------)
+--R a x
+--R +
+--R +--------------+
+--R +---+ | 2 2 +---+ +-+
+--R 2c x\|- a \|a x + b x + c + (- 2b x - 2c x)\|- a \|c
+--R /
+--R +--------------+
+--R +---+ +-+ | 2
+--R (a b x + 2a c)\|- a \|c \|a x + b x + c
+--R +
+--R 2 2 2 +---+
+--R (- 2a c x - 2a b c x - 2a c )\|- a
+--R ]
+--R Type: Union(List Expression
Integer,...)
+--E
+@
+
+\section{\cite{1}:14.293~~~~~$\displaystyle
+\int{\frac{dx}{x(ax^2+bx+c)^{3/2}}}$}
+$$\int{\frac{1}{x(ax^2+bx+c)^{3/2}}}=
+\frac{1}{c\sqrt{ax^2+bx+c}}
++\frac{1}{c}\int{\frac{1}{x\sqrt{ax^2+bx+c}}}
+-\frac{b}{2c}\int{\frac{1}{(ax^2+bx+c)^{3/2}}}
+$$
+<<*>>=
+)clear all
+
+--S 14 of 19
+aa:=integrate(1/(x*(a*x^2+b*x+c)^(3/2)),x)
+--R
+--R
+--R (1)
+--R +--------------+
+--R | 2 2 +-+
+--R ((b x + 2c)\|a x + b x + c + (- 2a x - 2b x - 2c)\|c )
+--R *
+--R +--------------+
+--R +-+ | 2
+--R 2\|c \|a x + b x + c - b x - 2c
+--R log(---------------------------------)
+--R +-+
+--R 2x\|c
+--R +
+--R +--------------+
+--R | 2 2 +-+
+--R 2b x\|a x + b x + c + (- 2a x - 2b x)\|c
+--R /
+--R +--------------+
+--R 2 +-+ | 2 2 2 2 3
+--R (b c x + 2c )\|c \|a x + b x + c - 2a c x - 2b c x - 2c
+--R Type: Union(Expression
Integer,...)
+--E
+@
+
+\section{\cite{1}:14.294~~~~~$\displaystyle
+\int{\frac{dx}{x^2(ax^2+bx+c)^{3/2}}}$}
+$$\begin{array}{rl}
+\displaystyle\int{\frac{1}{x^2(ax^2+bx+c)^{3/2}}}=
+&\displaystyle-\frac{ax^2+bx+c}{c^2x\sqrt{ax^2+bx+c}}\\
+&\\
+&\displaystyle+\frac{b^2-2ac}{2c^2}\int{\frac{1}{(ax^2+bx+c)^{3/2}}}\\
+&\\
+&\displaystyle-\frac{3b}{2c^2}\int{\frac{1}{x\sqrt{ax^2+bx+c}}}
+\end{array}
+$$
+<<*>>=
+)clear all
+
+--S 15 of 19
+aa:=integrate(1/(x^2*(a*x^2+b*x+c)^(3/2)),x)
+--R
+--R
+--R (1)
+--R +--------------+
+--R 3 3 2 2 2 +-+ | 2
+--R ((- 24a b c - 6b )x - 48b c x - 48b c x)\|c \|a x + b x + c
+--R +
+--R 2 4 2 3 3 2 2 2 3
+--R 24a b c x + (48a b c + 24b c)x + 72b c x + 48b c x
+--R *
+--R +--------------+
+--R +-+ | 2
+--R 2\|c \|a x + b x + c - b x - 2c
+--R log(---------------------------------)
+--R +-+
+--R 2x\|c
+--R +
+--R 3 3 2 2 2 2 3 +-+
+--R ((4a b c - 9b )x + (64a c - 24b c)x + 40b c x + 32c )\|c
+--R *
+--R +--------------+
+--R | 2
+--R \|a x + b x + c
+--R +
+--R 2 2 2 4 2 3 3 3 2 2
2
+--R (- 32a c + 24a b c)x + (- 48a b c + 24b c)x + (- 80a c + 8b c )x
+--R +
+--R 3 4
+--R - 56b c x - 32c
+--R /
+--R +--------------+
+--R 4 2 3 3 4 2 5 | 2
+--R ((16a c + 4b c )x + 32b c x + 32c x)\|a x + b x + c
+--R +
+--R 3 4 4 2 3 3 4 2 5 +-+
+--R (- 16a b c x + (- 32a c - 16b c )x - 48b c x - 32c x)\|c
+--R Type: Union(Expression
Integer,...)
+--E
+@
+
+\section{\cite{1}:14.295~~~~~$\displaystyle
+\int{(ax^2+bx+c)^{n+1/2}}~dx$}
+$$\begin{array}{rl}
+\displaystyle\int{(ax^2+bx+c)^{n+1/2}}=
+&\displaystyle\frac{(2ax+b)(ax^2+bx+c)^{n+1/2}}{4a(n+1)}\\
+&\\
+&\displaystyle+\frac{(2n+1)(4ac-b^2)}{8a(n+1)}
+\int{(ax^2+bx+c)^{n-1/2}}
+\end{array}
+$$
+<<*>>=
+)clear all
+
+--S 16 of 19
+aa:=integrate((a*x^2+b*x+c)^(n+1/2),x)
+--R
+--R
+--R 2n + 1
+--R x ------
+--R ++ 2 2
+--R (1) | (c + %N b + %N a) d%N
+--R ++
+--R Type: Union(Expression
Integer,...)
+--E
+@
+
+\section{\cite{1}:14.296~~~~~$\displaystyle
+\int{x(ax^2+bx+c)^{n+1/2}}~dx$}
+$$\int{x(ax^2+bx+c)^{n+1/2}}=
+\frac{(ax^2+bx+c)^{n+3/2}}{a(2n+3)}-
+\frac{b}{2a}\int{(ax^2+bx+c)^{n+1/2}}
+$$
+<<*>>=
+)clear all
+
+--S 17 of 19
+aa:=integrate(x*(a*x^2+b*x+c)^(n+1/2),x)
+--R
+--R
+--R 2n + 1
+--R x ------
+--R ++ 2 2
+--R (1) | %N (c + %N b + %N a) d%N
+--R ++
+--R Type: Union(Expression
Integer,...)
+--E
+@
+
+\section{\cite{1}:14.297~~~~~$\displaystyle
+\int{\frac{dx}{(ax^2+bx+c)^{n+1/2}}}$}
+$$\begin{array}{rl}
+\displaystyle\int{\frac{1}{(ax^2+bx+c)^{n+1/2}}}=
+&\displaystyle\frac{2(2ax+b)}{(2n-1)(4ac-b^2)(ax^2+bx+c)^{n-1/2}}\\
+&\\
+&\displaystyle
++\frac{8a(n-1)}{(2n-1)(4ac-b^2)}\int{\frac{1}{(ax^2+bx+c)^{n-1/2}}}
+\end{array}
+$$
+<<*>>=
+)clear all
+
+--S 18 of 19
+aa:=integrate(1/(a*x^2+b*x+c)^(n+1/2),x)
+--R
+--R
+--R x
+--R ++ 1
+--R (1) | ----------------------- d%N
+--R ++ 2n + 1
+--R ------
+--R 2 2
+--R (c + %N b + %N a)
+--R Type: Union(Expression
Integer,...)
+--E
+@
+
+\section{\cite{1}:14.298~~~~~$\displaystyle
+\int{\frac{dx}{x(ax^2+bx+c)^{n+1/2}}}$}
+$$\begin{array}{rl}
+\displaystyle\int{\frac{1}{x(ax^2+bx+c)^{n+1/2}}}=
+&\displaystyle\frac{1}{(2n-1)c(ax^2+bx+c)^{n-1/2}}\\
+&\\
+&\displaystyle
++\frac{1}{c}\int{\frac{1}{x(ax^2+bx+c)^{n-1/2}}}\\
+&\\
+&\displaystyle
+-\frac{b}{2c}\int{\frac{1}{(ax^2+bx+c)^{n+1/2}}}
+\end{array}
+$$
+<<*>>=
+)clear all
+
+--S 19 of 19
+aa:=integrate(1/(x*(a*x^2+b*x+c)^(n+1/2)),x)
+--R
+--R
+--R x
+--R ++ 1
+--R (1) | -------------------------- d%N
+--R ++ 2n + 1
+--R ------
+--R 2 2
+--R %N (c + %N b + %N a)
+--R Type: Union(Expression
Integer,...)
+--E
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp72-73
+\end{thebibliography}
+\end{document}
diff --git a/src/input/schaum14.input.pamphlet
b/src/input/schaum14.input.pamphlet
new file mode 100644
index 0000000..560ab37
--- /dev/null
+++ b/src/input/schaum14.input.pamphlet
@@ -0,0 +1,305 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum14.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.299~~~~~$\displaystyle
+\int{\frac{dx}{x^3+a^3}}$}
+$$\int{\frac{1}{x^3+a^3}}=
+\frac{1}{6a^2}\ln\frac{(x+a)^2}{x^2-ax+a^2}
++\frac{1}{a^2\sqrt{3}}\tan^{-1}\frac{2x-a}{a\sqrt{3}}
+$$
+<<*>>=
+)spool schaum14.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 12
+aa:=integrate(1/(x^3+a^3),x)
+--R
+--R
+--R +-+
+--R +-+ 2 2 +-+ (2x - a)\|3
+--R - \|3 log(x - a x + a ) + 2\|3 log(x + a) + 6atan(------------)
+--R 3a
+--R (1) ----------------------------------------------------------------
+--R 2 +-+
+--R 6a \|3
+--R Type: Union(Expression
Integer,...)
+--E
+@
+
+\section{\cite{1}:14.300~~~~~$\displaystyle
+\int{\frac{x~dx}{x^3+a^3}}$}
+$$\int{\frac{x}{x^3+a^3}}=
+\frac{1}{6a}\ln\frac{x^2-ax+a^2}{(x+a)^2}
++\frac{1}{a\sqrt{3}}\tan^{-1}\frac{2x-a}{a\sqrt{3}}
+$$
+<<*>>=
+)clear all
+
+--S 2 of 12
+aa:=integrate(x/(x^3+a^3),x)
+--R
+--R
+--R +-+
+--R +-+ 2 2 +-+ (2x - a)\|3
+--R \|3 log(x - a x + a ) - 2\|3 log(x + a) + 6atan(------------)
+--R 3a
+--R (1) --------------------------------------------------------------
+--R +-+
+--R 6a\|3
+--R Type: Union(Expression
Integer,...)
+--E
+@
+
+\section{\cite{1}:14.301~~~~~$\displaystyle
+\int{\frac{x^2~dx}{x^3+a^3}}$}
+$$\int{\frac{x^2}{x^3+a^3}}=
+\frac{1}{3}\ln(x^3+a^3)
+$$
+<<*>>=
+)clear all
+
+--S 3 of 12
+aa:=integrate(x^2/(x^3+a^3),x)
+--R
+--R
+--R 3 3
+--R log(x + a )
+--R (1) ------------
+--R 3
+--R Type: Union(Expression
Integer,...)
+--E
+@
+
+\section{\cite{1}:14.302~~~~~$\displaystyle
+\int{\frac{dx}{x(x^3+a^3)}}$}
+$$\int{\frac{1}{x(x^3+a^3)}}=
+\frac{1}{3a^3}\ln\left(\frac{x^3}{x^3+a^3}\right)
+$$
+<<*>>=
+)clear all
+
+--S 4 of 12
+aa:=integrate(1/(x*(x^3+a^3)),x)
+--R
+--R
+--R 3 3
+--R - log(x + a ) + 3log(x)
+--R (1) ------------------------
+--R 3
+--R 3a
+--R Type: Union(Expression
Integer,...)
+--E
+@
+
+\section{\cite{1}:14.303~~~~~$\displaystyle
+\int{\frac{dx}{x^2(x^3+a^3)}}~dx$}
+$$\int{\frac{1}{x^2(x^3+a^3)}}=
+-\frac{1}{a^3x}-\frac{1}{6a^4}\ln\frac{x^2-ax+a^2}{(x+a)^2}
+-\frac{1}{a^4\sqrt{3}}\tan^{-1}\frac{2x-a}{a\sqrt{3}}
+$$
+<<*>>=
+)clear all
+
+--S 5 of 12
+aa:=integrate(1/(x^2*(x^3+a^3)),x)
+--R
+--R
+--R (1)
+--R +-+
+--R +-+ 2 2 +-+ (2x - a)\|3
+-+
+--R - x\|3 log(x - a x + a ) + 2x\|3 log(x + a) - 6x atan(------------) -
6a\|3
+--R 3a
+--R
-----------------------------------------------------------------------------
+--R 4 +-+
+--R 6a x\|3
+--R Type: Union(Expression
Integer,...)
+--E
+@
+
+\section{\cite{1}:14.304~~~~~$\displaystyle
+\int{\frac{dx}{(x^3+a^3)^2}}$}
+$$\int{\frac{1}{(x^3+a^3)^2}}=
+\frac{x}{3a^3(x^3+a^3)}
++\frac{1}{9a^5}\ln\frac{(x+a)^2}{x^2-ax+a^2}
++\frac{2}{3a^5\sqrt{3}}\tan^{-1}\frac{2x-a}{a\sqrt{3}}
+$$
+<<*>>=
+)clear all
+
+--S 6 of 12
+aa:=integrate(1/(x^3+a^3)^2,x)
+--R
+--R
+--R (1)
+--R 3 3 +-+ 2 2 3 3 +-+
+--R (- x - a )\|3 log(x - a x + a ) + (2x + 2a )\|3 log(x + a)
+--R +
+--R +-+
+--R 3 3 (2x - a)\|3 2 +-+
+--R (6x + 6a )atan(------------) + 3a x\|3
+--R 3a
+--R /
+--R 5 3 8 +-+
+--R (9a x + 9a )\|3
+--R Type: Union(Expression
Integer,...)
+--E
+@
+
+\section{\cite{1}:14.305~~~~~$\displaystyle
+\int{\frac{x~dx}{(x^3+a^3)^2}}$}
+$$\int{\frac{x}{(x^3+a^3)^2}}=
+\frac{x^2}{3a^3(x^3+a^3)}
++\frac{1}{18a^4}\ln\frac{x^2-ax+a^2}{(x+a)^2}
++\frac{1}{3a^4\sqrt{3}}\tan^{-1}\frac{2x-a}{a\sqrt{3}}
+$$
+<<*>>=
+)clear all
+
+--S 7 of 12
+aa:=integrate(x/(x^3+a^3)^2,x)
+--R
+--R
+--R (1)
+--R 3 3 +-+ 2 2 3 3 +-+
+--R (x + a )\|3 log(x - a x + a ) + (- 2x - 2a )\|3 log(x + a)
+--R +
+--R +-+
+--R 3 3 (2x - a)\|3 2 +-+
+--R (6x + 6a )atan(------------) + 6a x \|3
+--R 3a
+--R /
+--R 4 3 7 +-+
+--R (18a x + 18a )\|3
+--R Type: Union(Expression
Integer,...)
+--E
+@
+
+\section{\cite{1}:14.306~~~~~$\displaystyle
+\int{\frac{x^2~dx}{(x^3+a^3)^2}}$}
+$$\int{\frac{x^2}{(x^3+a^3)^2}}=
+-\frac{1}{3(x^3+a^3)}
+$$
+<<*>>=
+)clear all
+
+--S 8 of 12
+aa:=integrate(x^2/(x^3+a^3)^2,x)
+--R
+--R
+--R 1
+--R (1) - ---------
+--R 3 3
+--R 3x + 3a
+--R Type: Union(Expression
Integer,...)
+--E
+@
+
+\section{\cite{1}:14.307~~~~~$\displaystyle
+\int{\frac{dx}{x(x^3+a^3)^2}}$}
+$$\int{\frac{1}{x(x^3+a^3)^2}}=
+\frac{1}{3a^3(x^3+a^3)}+\frac{1}{3a^6}\ln\left(\frac{x^3}{x^3+a^3}\right)
+$$
+<<*>>=
+)clear all
+
+--S 9 of 12
+aa:=integrate(1/(x*(x^3+a^3)^2),x)
+--R
+--R
+--R 3 3 3 3 3 3 3
+--R (- x - a )log(x + a ) + (3x + 3a )log(x) + a
+--R (1) ------------------------------------------------
+--R 6 3 9
+--R 3a x + 3a
+--R Type: Union(Expression
Integer,...)
+--E
+@
+
+\section{\cite{1}:14.308~~~~~$\displaystyle
+\int{\frac{dx}{x^2(x^3+a^3)^2}}~dx$}
+$$\int{\frac{1}{x^2(x^3+a^3)^2}}=
+-\frac{1}{a^6x}-\frac{x^2}{3a^6(x^3+a^3)}
+-\frac{4}{3a^6}\int{\frac{x}{x^3+a^3}}
+$$
+<<*>>=
+)clear all
+
+--S 10 of 12
+aa:=integrate(1/(x^2*(x^3+a^3)^2),x)
+--R
+--R
+--R (1)
+--R 4 3 +-+ 2 2 4 3 +-+
+--R (- 2x - 2a x)\|3 log(x - a x + a ) + (4x + 4a x)\|3 log(x + a)
+--R +
+--R +-+
+--R 4 3 (2x - a)\|3 3 4 +-+
+--R (- 12x - 12a x)atan(------------) + (- 12a x - 9a )\|3
+--R 3a
+--R /
+--R 7 4 10 +-+
+--R (9a x + 9a x)\|3
+--R Type: Union(Expression
Integer,...)
+--E
+@
+
+\section{\cite{1}:14.309~~~~~$\displaystyle
+\int{\frac{x^m~dx}{x^3+a^3}}$}
+$$\int{\frac{x^m}{x^3+a^3}}=
+\frac{x^{m-2}}{m-2}-a^3\int{\frac{x^{m-3}}{x^3+a^3}}
+$$
+<<*>>=
+)clear all
+
+--S 11 of 12
+aa:=integrate(x^m/(x^3+a^3),x)
+--R
+--R
+--R x m
+--R ++ %L
+--R (1) | -------- d%L
+--R ++ 3 3
+--R a + %L
+--R Type: Union(Expression
Integer,...)
+--E
+@
+
+\section{\cite{1}:14.310~~~~~$\displaystyle
+\int{\frac{dx}{x^n(x^3+a^3)}}$}
+$$\int{\frac{1}{x^n(x^3+a^3)}}=
+\frac{-1}{a^3(n-1)x^{n-1}}-\frac{1}{a^3}\int{\frac{1}{x^{n-3}(x^3+a^3)}}
+$$
+<<*>>=
+)clear all
+
+--S 12 of 12
+aa:=integrate(1/(x^n*(x^3+a^3)),x)
+--R
+--R
+--R x
+--R ++ 1
+--R (1) | ------------- d%L
+--R ++ 3 3 n
+--R (a + %L )%L
+--R Type: Union(Expression
Integer,...)
+--E
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 p73
+\end{thebibliography}
+\end{document}
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